7x^2-22x-34=0

Solution for 7x^2-22x-34=0 equation:

7x^2-22x-34=0

a = 7; b = -22; c = -34;
Δ = b2-4ac
Δ = -222-4·7·(-34)
Δ = 1436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1436}=\sqrt{4*359}=\sqrt{4}*\sqrt{359}=2\sqrt{359}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{359}}{2*7}=\frac{22-2\sqrt{359}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{359}}{2*7}=\frac{22+2\sqrt{359}}{14}
$